Weighted Estimates of the Fractional Type Marcinkiewicz Integral and Its Commutator on Morrey–Guliyev Spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050274

X. J. Zhu, S. P. Tao

引用次数: 0

Abstract

The aim of this paper is to study weighted estimates of the fractional type Marcinkiewicz integral and its commutator. By producing Guliyev type local pointwise estimates, we prove the boundedness of the fractional type Marcinkiewicz integral on the weighted Morrey–Guliyev spaces. Meanwhile, we also consider the corresponding weighted estimates of the commutators generated by a Lipschitz function and a BMO function.

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莫雷-古利耶夫空间上的分数型马钦凯维奇积分及其换元器的加权估计值

摘要本文旨在研究分数型 Marcinkiewicz 积分及其换元的加权估计。通过产生 Guliyev 型局部点估计，我们证明了分数型 Marcinkiewicz 积分在加权 Morrey-Guliyev 空间上的有界性。同时，我们还考虑了由 Lipschitz 函数和 BMO 函数产生的换元器的相应加权估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.